The Gauss Pseudospectral Method is used to design the optimal reentry trajectory of the hypersonic vehicle to maximize the range under the heating rate, dynamic pressure and overload constraints. The indirect methods for solving the optimal control problems is to solve the necessary conditions by applying the Pontryagin minimum principle, which is difficult for solving the Two Points Boundary Value Problem. In this paper, the problem is transformed into a nonlinear programming problem (NLP) at the discrete points subject to continuous state equality and inequality constraints. The differential of the state can be expressed as the linear combination of the values at the discrete points approximately. Therefore, the dynamic equations can be transformed into the algebraic equations and the cost function is also expressed as the function of the states and control. The NLP can be solved by the sequential quadratic programming method. The proposed method is compared with the control parametrization method and the first one has the longer range than that of the second one.
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